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Nonstationary Gabor frames — Existence and construction

Monika Dörfler

Department of Mathematics, NuHAG, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

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and

Ewa Matusiak

Department of Mathematics, NuHAG, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

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https://doi.org/10.1142/S0219691314500325Cited by:15 (Source: Crossref)

Abstract

Nonstationary Gabor frames were recently introduced in adaptive signal analysis. They represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper, we show a general existence result for this family of frames. Then, we give a perturbation result for nonstationary Gabor frames and construct nonstationary Gabor frames with non-compactly supported windows from a related painless nonorthogonal expansion. Finally, the theoretical results are illustrated by two examples of practical relevance.

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